Struct MaxCut 

pub struct MaxCut<G, W> { /* private fields */ }

The Maximum Cut problem.

Given a weighted graph G = (V, E) with edge weights w_e, find a partition of V into sets S and V\S such that the total weight of edges crossing the cut is maximized.

Representation

Each vertex is assigned a binary value:

• 0: vertex is in set S
• 1: vertex is in set V\S

An edge contributes to the cut if its endpoints are in different sets.

Type Parameters

• G - The graph type (e.g., SimpleGraph, KingsSubgraph, UnitDiskGraph)
• W - The weight type for edges (e.g., i32, f64)

Example

use problemreductions::models::graph::MaxCut;
use problemreductions::topology::SimpleGraph;
use problemreductions::types::SolutionSize;
use problemreductions::{Problem, Solver, BruteForce};

// Create a triangle with unit weights
let graph = SimpleGraph::new(3, vec![(0, 1), (1, 2), (0, 2)]);
let problem = MaxCut::new(graph, vec![1, 1, 1]);

// Solve with brute force
let solver = BruteForce::new();
let solutions = solver.find_all_best(&problem);

// Maximum cut in triangle is 2 (any partition cuts 2 edges)
for sol in solutions {
    let size = problem.evaluate(&sol);
    assert_eq!(size, SolutionSize::Valid(2));
}

Implementations

impl<G: Graph, W: Clone + Default> MaxCut<G, W>

pub fn new(graph: G, edge_weights: Vec<W>) -> Self

Create a MaxCut problem from a graph with specified edge weights.

Arguments

• graph - The underlying graph
• edge_weights - Weights for each edge (must match graph.num_edges())

pub fn unweighted(graph: G) -> Self

where W: From<i32>,

Create a MaxCut problem with unit weights.

pub fn graph(&self) -> &G

Get a reference to the underlying graph.

pub fn edges(&self) -> Vec<(usize, usize, W)>

Get the edges with weights.

pub fn edge_weight_by_index(&self, idx: usize) -> Option<&W>

Get the weight of an edge by its index.

pub fn edge_weight(&self, u: usize, v: usize) -> Option<&W>

Get the weight of an edge between vertices u and v.

pub fn edge_weights(&self) -> Vec<W>

Get edge weights only.

pub fn cut_size(&self, config: &[usize]) -> W::Sum

where W: WeightElement,

Compute the cut size for a given partition configuration.

impl<G: Graph, W: WeightElement> MaxCut<G, W>

pub fn num_vertices(&self) -> usize

Get the number of vertices in the underlying graph.

pub fn num_edges(&self) -> usize

Get the number of edges in the underlying graph.

Trait Implementations

impl<G: Clone, W: Clone> Clone for MaxCut<G, W>

fn clone(&self) -> MaxCut<G, W>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<G: Debug, W: Debug> Debug for MaxCut<G, W>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de, G, W> Deserialize<'de> for MaxCut<G, W>

where G: Deserialize<'de>, W: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<G, W> OptimizationProblem for MaxCut<G, W>

where G: Graph + VariantParam, W: WeightElement + VariantParam,

type Value = <W as WeightElement>::Sum

The inner objective value type (e.g., i32, f64).

fn direction(&self) -> Direction

Whether to maximize or minimize the metric.

impl<G, W> Problem for MaxCut<G, W>

where G: Graph + VariantParam, W: WeightElement + VariantParam,

const NAME: &'static str = "MaxCut"

Base name of this problem type (e.g., “MaximumIndependentSet”).

type Metric = SolutionSize<<W as WeightElement>::Sum>

The evaluation metric type.

fn variant() -> Vec<(&'static str, &'static str)>

Returns variant attributes derived from type parameters.

fn dims(&self) -> Vec<usize>

Configuration space dimensions. Each entry is the cardinality of that variable.

fn evaluate(&self, config: &[usize]) -> SolutionSize<W::Sum>

Evaluate the problem on a configuration.

fn num_variables(&self) -> usize

Number of variables (derived from dims).

impl ReduceTo<MaxCut<SimpleGraph, i32>> for SpinGlass<SimpleGraph, i32>

type Result = ReductionSGToMaxCut<i32>

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl ReduceTo<SpinGlass<SimpleGraph, i32>> for MaxCut<SimpleGraph, i32>

type Result = ReductionMaxCutToSG<i32>

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl<G, W> Serialize for MaxCut<G, W>

where G: Serialize, W: Serialize,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl DeclaredVariant for MaxCut<SimpleGraph, i32>